Google Maps - Map Projection

Map Projection

Google Maps is based on a close variant of the Mercator projection. If the Earth were perfectly spherical, the projection would be the same as the Mercator. Google Maps uses the formulæ for the spherical Mercator, but the coordinates of features on Google Maps are the GPS coordinates based on the WGS 84 datum. The difference between a sphere and the WGS 84 ellipsoid causes the resultant projection not to be precisely conformal. The discrepancy is imperceptible at the global scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale.

Assuming that and are the components of infinitesmal local ENU coordinates, their breadth and length projected on the map are described as follows:

\begin{align} & dx = a_\text{map} \left(\frac{a}{\sqrt{1-e^2 \sin^2 \varphi }}\right)^{-1} \sec \varphi \, dE ,\\ & dy = a_\text{map} \left(\frac{a(1- e^2)}{\left(1-e^2 \sin^2 \varphi\right)^{3/2}}\right)^{-1} \sec \varphi \, dN, \end{align}

where is geodetic latitude, is the first eccentricity of the ellipsoid of the Earth, is the semi-major axis of the Earth, and is that at the scale of the map as drawn (see "Geodetic system" and "Mercator projection"). Google Maps uses

a_\text{map} = \frac{256 \times 2^{zoomLevel}}{2 \pi} \ \text{pixels} .

Because the Mercator projects the poles at infinity, Google Maps cannot show the poles. Instead it cuts off coverage at 85° north and south. This is not considered a limitation, given the purpose of the service.

Read more about this topic:  Google Maps

Famous quotes containing the words map and/or projection:

    “In thy face I see
    The map of honor, truth, and loyalty.”
    —William Shakespeare (1564–1616)

    “In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
    —Nelson Goodman (b. 1906)